Does anyone know whether moving my blog to this service http://www.hostgator.com/apps/wordpress-hosting.shtml (HostGator), using their WordPress hosting, would allow me to put advertisements on my blog? or would I need to not use the WordPress hosting feature to be able to do that? Any advice will help.
You would have to check with hostgator on any of their terms of service, however, as a general rule, if someone wants to have advertisements on their blog, they use a wordpress.org install on another host. I would think that you would be able to have advertising on your own wordpress.org install.